If the first term of a harmonic progression is 5 and the second term is 10, what is the third term?
Practice Questions
1 question
Q1
If the first term of a harmonic progression is 5 and the second term is 10, what is the third term?
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The reciprocals are 1/5 and 1/10. The common difference is -1/10. The third term's reciprocal will be 1/10 - 1/10 = 1/15, so the third term is 15.
Questions & Step-by-step Solutions
1 item
Q
Q: If the first term of a harmonic progression is 5 and the second term is 10, what is the third term?
Solution: The reciprocals are 1/5 and 1/10. The common difference is -1/10. The third term's reciprocal will be 1/10 - 1/10 = 1/15, so the third term is 15.
Steps: 9
Step 1: Identify the first term of the harmonic progression (HP), which is 5.
Step 2: Identify the second term of the harmonic progression (HP), which is 10.
Step 3: Find the reciprocals of the first and second terms. The reciprocal of 5 is 1/5, and the reciprocal of 10 is 1/10.
Step 4: Calculate the common difference between the reciprocals. Subtract 1/5 from 1/10.
Step 5: To subtract, convert 1/5 to a fraction with a common denominator of 10. This gives us 2/10.
Step 6: Now subtract: 1/10 - 2/10 = -1/10. This is the common difference.
Step 7: To find the third term's reciprocal, take the second term's reciprocal (1/10) and subtract the common difference (-1/10).
